A053152 Number of 2-element intersecting families whose union is an n-element set.
0, 2, 9, 32, 105, 332, 1029, 3152, 9585, 29012, 87549, 263672, 793065, 2383292, 7158069, 21490592, 64504545, 193579172, 580868589, 1742867912, 5229128025, 15688432652, 47067395109, 141206379632, 423627527505, 1270899359732, 3812731633629, 11438262009752
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (in Russian), Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
- V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
- Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
Programs
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Magma
[Floor((3^n-2^n)/2): n in [1..30]]; // Vincenzo Librandi, Mar 17 2015
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Maple
A053152:=n->floor((3^n-2^n)/2): seq(A053152(n), n=1..30); # Wesley Ivan Hurt, Mar 19 2015
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Mathematica
CoefficientList[Series[x (2 - 3 x) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 17 2015 *) LinearRecurrence[{6,-11,6}, {0,2,9}, 50] (* G. C. Greubel, Oct 06 2017 *) -
PARI
for(n=1,50, print1((1/2)*(3^n -2^n -1), ", ")) \\ G. C. Greubel, Oct 06 2017
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Sage
[(3^n - 1)/2-2^(n-1) for n in range(1,27)] # Zerinvary Lajos, Jun 05 2009
Formula
a(n) = (1/2!)*(3^n-2^n-1).
From Colin Barker, Jun 26 2012: (Start)
a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3).
G.f.: x^2*(2-3*x)/((1-x)*(1-2*x)*(1-3*x)). (End)
a(n) = floor((3^n-2^n)/2). - Wesley Ivan Hurt, Mar 16 2015
Extensions
More terms from James Sellers, Mar 01 2000
a(27)-a(28) from Vincenzo Librandi, Mar 17 2015